The steady application of quantitative easing (QE ) has been followed by big and nonmonotonic effects on international asset prices and capital flows. We rationalize these observations in a model in which a central bank buys domestic assets that serve as the best collateral for investors worldwide. The crucial insight is that domestic private agents adjust their portfolios of domestic and foreign assets in different ways to offset QE, conditional on whether they are (i) fully leveraged, (ii ) partially leveraged, or (iii) unleveraged. These portfolio shifts can diminish or even reverse the impact of ever-larger QE interventions on asset prices. (JEL E31, E32, E43, E44, E52, E58, F34)